You can write an equation of a line if you know its slope and the coordinates of one point on the line.
This
equation is said to be in point-slope form. Recall that it is called a linear
equation because its graph is a straight line. The graph of a nonlinear equation is
not a straight line.
Example
Write the
point-slope form of an equation for each line passing through the given point
and having the given slope
An equation of the
line is 
.
Check: Look at the graph. Choose some other point
on
and determine whether it is a solution of
. Try (0, –8).
You can also write an equation of a line if you know the
coordinates of two points on the line.
Example
2.
Write the point-slope form of an equation of the line at the right.
Alternative Solutions:
First, determine the
slope of the line.
The slope is 
. Now use the slope and either point to write an equation.
Method 1 Use (–2, 5).
Check:
Method 2 Use (3, 1).
Check:
Both 
and 
are point-slope forms of
an equation for the line passing through (3, 1) and (–2, 5).
Example
Sports Link
3.
In the 1988 Olympics, the women’s winning long jump was about 24.7 feet. It
is predicted that by 2020 the record will be about 26.3 feet. Write the point-slope
form of an equation for the line in the graph.
Alternative Solutions:
First, determine the
slope of the line.
Now use the slope and
either point to write an equation.
An equation of the line
is 
.
Check by substituting
(2020, 26.3) into the equation.
Sumber
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